factorise: 2x² - x - 3​

===================================================

Work Shown:

[tex]33^{-1} \equiv 77 \text{ (mod 508)}\\\\(3*11)^{-1} \equiv 77 \text{ (mod 508)}\\\\3^{-1}*11^{-1} \equiv 77 \text{ (mod 508)}\\\\3*3^{-1}*11^{-1} \equiv 3*77 \text{ (mod 508)}\\\\11^{-1} \equiv 231 \text{ (mod 508)}\\\\[/tex]

Notice how 33*77 = 2541 and 11*231 = 2541

[tex]2541 \equiv 1 \text{ (mod 508)}[/tex] since 2541/508 has a remainder of 1.

So effectively [tex]33*77 \equiv 1 \text{ (mod 508)}[/tex] and [tex]11*231 \equiv 1 \text{ (mod 508)}[/tex]

Answer:

[tex]\boxed{40}[/tex]

Step-by-step explanation:

Divide 22/55 to get 0.4.

Multiply 0.4 * 100 to get 40.

That value is your percentage.

Answer:

40 percent

Step-by-step explanation:

22/55

simplify by 11

2/5

multiply by 20

40/100

turn to percent

40 percent

Answer:

log_e (7)

Step-by-step explanation:

(ln) 7,

ln stands for natural log, which is log base e

log_e (7)

Answer:

2¹ + 3¹, 2³ - 2¹, 3²

Step-by-step explanation:

2³ - 2¹ = 8 - 2 = 6

2¹ + 3¹ = 2 + 3 = 5

3² = 9

Answer:

Step-by-step explanation:

Given the expression, -3(2w+6)-4, we are to look for an equivalent expression for the equation.This is as shown:

Step 1: Open the parenthesis

= -3(2w+6)-4

= -3(2w)-3(6)-4

= -6w-18-4

Step 2: Simplify the resulting expression in step 1

= -6w-18-4

= -6w - 22

Step 3: factor out the common values from each term. Since the common value is 2, on factoring we will have;

2{-3w+(-11)}

Hence the equivalent expression is 2{-3w+(-11)}

Answer:

a and b

Step-by-step explanation:

no.

Answer:

3

Step-by-step explanation:

Answer:

$3 per guest

Step-by-step explanation:

18/6

= 3

Answer:

Step-by-step explanation:

First you want to find the slope

y2-y1/x2-x1

7-(-3)/8-(-3)

Two negatives equal a positive. so Rewrite

7+3/8+3

10/11

Slope=10/11

To find the equation of the line..

y-y1=10/11(x-x1)

y-(-3)=10/11(x-(-3)

Again double negative, so rewrite

y+3=10/11(x+3)

y+3=10/11x+30/11

Subtract three from both sides to isolate 'y'

y+3-3=10/11x+30/11-3

y=10/11x+30/11-3

y=10/11x-3/11

Answer:

[tex]d = \sqrt{(x2 - x1) {}^{2} + (y2 - y1) {}^{2} }[/tex]

Step-by-step explanation:

[tex]d = \sqrt{( - 4 + 3) {}^{2} + (7 - 9) {}^{2} } [/tex]

[tex]d = \sqrt{(1 + 4)} = \sqrt{5} [/tex]

Answer:

the answer is 44

Step-by-step explanation:

4*2=8

48-(32:8)

48-(4)

44

I really hope it helps:))))))))))

Answer:

C. 32

Step-by-step explanation:

Order of Operations: Multiplication/Division (left to right) comes before Addition/Subtraction (left to right).

48 - 32/4 x 2 (Division)

48 - 8 x 2 (Multiplication)

48 - 16 (Subtraction)

32

Answer:

-11 and -10

Step-by-step explanation:

● -√120 = -1 × √120

● -√120 = -1 × 2√30

● 30 is close to 25 so √30 is close to five but greater than it.

Multiplying 5 by -2 gives -10

Multipluing √30 by -2 gives you a number that is close to -10 but smaller than it.

So -√120 lies between -11 and -10

Answer:

y=2x-4

Step-by-step explanation:

The slope of the line is 2 and y intercept is - 4. The equation will be y=2x-4

Answer:

6000 metres is equal to 6 kilograms

Answer as an inequality:  [tex]x > 0[/tex]

Answer in interval notation:  [tex](0, \infty)[/tex]

Answer in words: Set of positive real numbers

All three represent the same idea, but in different forms.

======================================================

Explanation:

Any log is the inverse of an exponential equation. Consider a general base b such that f(x) = b^x. The inverse of this is [tex]f^{-1}(x) = \log_b(x)[/tex]

For the exponential b^x, we cannot have b^x = 0. We can get closer to it, but we can't actually get there. The horizontal asymptote is y = 0.

Because of this, [tex]\log_b(x)[/tex] has a vertical asymptote x = 0 (recall that x and y swap, so the asymptotes swap as well). This means we can get closer and closer to x = 0 from the positive side, but never reach x = 0 itself.

The domain of [tex]\log_b(x)[/tex] is x > 0 which in interval notation would be [tex](0, \infty)[/tex]. This is the interval from 0 to infinity, excluding both endpoints.

------------------------

The natural log function Ln(x) is a special type of log function where the base is b = e = 2.718 approximately.

So,

[tex]\log_e(x) = \text{Ln}(x)[/tex]

allowing all of what was discussed in the previous section to apply to this Ln(x) function as well.

------------------------

In short, the domain is the set of positive real numbers. We can't have x be 0 or negative.

Answer:

0.47 yes, 0.1666... yes, 0.5473 no, 0.541 yes

Step-by-step explanation:

0.47 yes: is a repeating decimal

0.1666... yes: is a repeating decimal

0.5473 no: is neither terminating or repeating

0.541 yes: is terminating

Answer:

probability that the card is a Queen or a diamond= 0.3269

Step-by-step explanation:

There are 4 queen in a deck of cards and 13 diamond in a deck of cards.

And a deck of cards contains 52 cards total.

Probability of the card selected to be a queen = number of queen/total number of cards

Probability of the card selected to be a queen =4/52

Probability of the card selected to be a queen= 1/13

Probability of the card selected to be a diamond= number of diamond/ total number of cards

Probability of the card selected to be a diamond=13/52

Probability of the card selected to be a diamond=1/4

probability that the card is a Queen or a diamond= Probability of the card selected to be a queen + Probability of the card selected to be a diamond

probability that the card is a Queen or a diamond= 1/13+1/4

probability that the card is a Queen or a diamond= 0.3269

Answer:

[tex]f(x) = 5 - (x - 4)^2[/tex].

Step-by-step explanation:

[tex]f(x) = 5 - (x - 4)^2[/tex]

[tex]f(x) = 5 - (x-4)*(x-4)[/tex]

[tex]f(x) = 5 - (x^2 - 4x - 4x + 16)[/tex]

[tex]f(x) = 5 - (x^2 - 8x + 16)[/tex]

[tex]f(x) = 5 - x^2 + 8x - 16[/tex]

[tex]f(x) = -x^2 + 8x - 11[/tex].

Hope this helps!

Answer:

y = 9x - 59

Step-by-step explanation:

y - 4= 9(x-7)

y - 4 = 9x - 63

y - 4 + 4 = 9x - 63 + 4

y = 9x - 59

Answer:

Below

Step-by-step explanation:

● y-4 = 9(x-7)

Multiply 9 by (x-7)

● y-4 = 9x - 63

Add 4 to both sides

● y-4+4 = 9x-63 +4

● y = 9x - 59

Answer:

x = 17

Step-by-step explanation:

-2x + 8 = -26

Subtract 8 from each side

-2x + 8-8 = -26-8

-2x = -34

Divide each side by -2

-2x/-2 = -34/-2

x = 17

Answer:

The answer is x=17

Step-by-step explanation:

−2x+8−8=−26−8

−2x=−34

−2x /−2 = −34 /−2

x=17

Answer:

212m

Step-by-step explanation:

The set up will be equivalent to a right angled triangle where the height is the opposite side facing the 45° angle directly. The length of the rope will be the slant side which is the hypotenuse.

Using the SOH, CAH, TOA trigonometry identity to solve for the length of the rope;

Since we have the angle theta = 45° and opposite = 150m

According to SOH;

Sin theta = opposite/hypotenuse.

Sin45° = 150/hyp

hyp = 150/sin45°

hyp = 150/(1/√2)

hyp = 150×√2

hyp = 150√2 m

hyp = 212.13m

Hence the length of the rope for the kite sail, in order to pull the ship at an angle of 45° and be at a vertical height of 150 m is approximately 212m

By applying trigonometry ratio, the length of the rope for the kite to sail would be: 212 m.

Recall:

The diagram describing the situation is attached below (see attachment).

Thus:

The reference angle [tex](\theta) = 45^{\circ}[/tex]

Let the length of the rope be x = Hypotenuse

Opposite = 150 m

To find the length of the rope (x), apply SOH

Thus:

[tex]Sin(\theta) = \frac{Opp}{Hyp}[/tex]

[tex]Sin(45) = \frac{150}{x}[/tex]

[tex]x \times Sin(45) = \frac{150}{x} \times x\\\\x \times Sin(45) = 150[/tex]

[tex]\frac{x \times Sin(45)}{Sin(45)} = \frac{150}{ Sin(45)} \\\\\mathbf{x = 212 $ m}[/tex]

Therefore, by applying trigonometry ratio, the length of the rope for the kite to sail would be: 212 m.

Learn more here:

https://brainly.com/question/12718789

Al plantear un sistema de ecuaciones lineales, encontramos que el número de obreros que contrató el ingeniero civil fue 50.

Para encontrar el número de obreros que el ingeniero contrató debemos plantear un sistema de ecuaciones lineales de dos ecuaciones con dos incógnitas, tal como sigue:

[tex] M - 1400*x = -8000 [/tex]   (1)

[tex] M - 1200*x = 2000 [/tex]   (2)

En donde:

M: es la incógnita igual al monto de dinero del ingeniero

x: es la incógnita igual al número de obreros

De la ecuación (1) tenemos:

[tex] M = 1400*x - 8000 [/tex]   (3)

Podemos encontrar el valor de x (número de obreros), introduciendo la ecuación (3) en la ec (2):

[tex] 1400*x - 8000 - 1200*x = 2000 [/tex]

[tex] 200*x = 10000 [/tex]

[tex] x = 50 [/tex]

El monto de dinero inicial del ingeniero sería entonces (ec 3):

[tex] M = 1400*50 - 8000 = 62000 [/tex]

Por lo tanto, el número de obreros que contrató el ingeniero es 50.

Puedes aprender sobre otro método de resolución de sistemas de ecuaciones lineales ingresando acá: https://brainly.com/question/10831551?referrer=searchResults                                    

Espero que te sea de utilidad!

Answer:

(-2y-6)(-3y-8)

= 6y²+16y+18y+48

= 6y²+ 34 y +48

Hope this helps

if u have question let me know in comments ^_^

Answer:

Here is your answer!!!

Step-by-step explanation:

-2y(-3y-8)-6(-3y-8)

6y^2+16y+18y+48

6y^2+34y+48

Answer:

16+74

Step-by-step explanation:

substitute 16 into the equation

Answer:

196 degrees

Step-by-step explanation:

360-164=196 degrees

the arch CDF=2*82=164

so the arch CGF =360-164=196 degrees

Answer:

A = 120, P = 55

Step-by-step explanation:

Triangle

Area = (bh)/2

A = (20x12)/2

A =240/2

A = 120

Perimeter = a + b + c

to find c, use a^2 +b^2 = c^2

20^2 + 12^2 = c^2

400 + 144 = c^2

544 = c^2

c = about 23

20 + 12 + 23 = 55

Answer:

t=0.64

Step-by-step explanation:

h = -16t^2 +4t +4

We want h =0 since it is hitting the ground

0 = -16t^2 +4t +4

Using the quadratic formula

a = -16  b = 4  c=4

-b ± sqrt( b^2 -4ac)

----------------------------

         2a

-4 ± sqrt( 4^2 -4(-16)4)

----------------------------

         2(-16)

-4 ± sqrt( 16+ 256)

----------------------------

         -32

-4 ± sqrt( 272)

----------------------------

         -32

-4 ± sqrt( 16*17)

----------------------------

         -32

-4 ± sqrt( 16) sqrt(17)

----------------------------

         -32

-4 ± 4 sqrt(17)

----------------------------

         -32

Divide by -4

1 ±  sqrt(17)

----------------------------

         8

To the nearest hundredth

t=-0.39

t=0.64

Since time cannot be negative

t=0.64

Answer:

0.64  

Step-by-step explanation:

0 = -16t^2 + 4t + 4

-4(4t^2 - t -1) = 0

t = [-(-1) +/- sqrt (1 - 4*4*-1)] / 8)

t = 0.64, -0.39

answer is 0.64

Answer:

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur.

Probability = Expected outcome/Total outcome

Since we are to find the probability that 2 randomly selected points from Q,R,S,T and W are non-collinear

Non collinear points are points that doesn't lie on the same straight line. From the diagram given, the two point that are non colliear are (QR, QS, QT and QW making 4 2random non collinear points. Hence out expected number of outcome is 4.

For the total possible outcome, we are to find the number of ways we can randomly select two points from the 5 points given and this can be done using the combination rule.

This can therefore be done in 5C2 number of ways.

5C2 = 5!/(5-2)!2!

5C2 = 5!/3!2!

5C2 = 5*4*3*2*1/3*2*2

5C2 = 5*2

5C2 = 10 different ways

Hence the total possible outcome is 10

Therefore, the probability that 2 randomly selected points from Q,R,S,T and W are noncollinear will be 4/10 = 2/5

Answer:

y = 3/4x + 2

Step-by-step explanation:

to find the slope its rise over run and you go up 3 and run 4 to get 3/4. then you just look on the y axis and see that the line passes 2. so that is the answer

Answer:

x = 4

Step-by-step explanation:

x * 5 = 20 * 1

x = 4

Answer:

[tex]\boxed{x=4}[/tex]

Step-by-step explanation:

Hey there!

Well to solve for x we need to cross multiply,

x/20 = 1/5

5x = 20

Divide both sides by 5

x = 4

Hope this helps :)